Bootstrap and Other Resampling Methodologies in Statistics of Extremes

In Statistics of Extremes the estimation of parameters of extreme or even rare events is usually done under a semi-parametric framework. The estimators are based on the largest k ordered statistics in the sample or on the excesses over a high level u and although showing good asymptotic properties, most of them present a strong dependence on k or u with high bias when the k increases or the level u decreases. The use of resampling methodologies has revealed to be promising in the reduction of the bias and in the choice of k or u. Different approaches for resampling need to be considered depending on whether we are in an independent or in a dependent setup. A great amount of investigation has been performed for the independent situation. The ∗Research partially supported by National Funds through FCT—Fundação para a Ciência e a Tecnologia, projects PEst-OE/MAT/UI0006/2011, PEstOE/AGR/UI0239/2011, PTDC/FEDER and CMA.